We obtain subordination and superordination preserving properties for the Saigo type generalized fractional differ-integral operator, defined for multivalent functions in the open unit disk. A differential sandwich-type theorem for these multivalent function, and some consequences are also presented.

Fractional (non-integer) derivatives and integrals play an important role in theory and applications. The fractional calculus of variations is a rather recent subject with the first results from 1996. This paper presents necessary and sufficient optimality conditions for fractional problems of the calculus of variations with a Lagrangian density depending on the free end-points. The fractional ...

A class of fractional derivative operators (with the Appell hypergeometric function in the kernel) is used here to define a new subclass of analytic functions and a coefficient bound inequality is established for this class of functions. Also, an inclusion theorem for a class of fractional integral operators involving the Hardy space of analytic functions is proved. The concluding remarks brief...

in this paper an approximate analytical solution of the fractional zakharov-kuznetsov equations will be obtained with the help of the reduced differential transform method (rdtm). it is in-dicated that the solutions obtained by the rdtm are reliable and present an effective method for strongly nonlinear fractional partial differential equations.

In recent years, many works on the subject of fractional calculus contain interesting accounts of the theory and applications of fractional calculus operators in a number of areas of mathematical analysis ( such as ordinary and partial differential equations, integral equations, summation of series, etc.). The main object of this paper is to construct multivariable extension of Jacobi polynomia...

This report is aimed at the engineering and/or scientific professional who wishes to learn about Fractional Calculus and its possible applications in his/her field(s) of study. The intent is to first expose the reader to the concepts, applicable definitions, and execution of fractional calculus (including a discussion of notation, operators, and fractional order differential equations), and sec...

In this paper we aim to construct an abstract model of a differential operator with fractional integro-differential composition in final terms, where modeling is understood as interpretation concrete operators terms the infinitesimal generator corresponding semigroup. We study such Kipriyanov operator, Riesz potential, difference operator. Along this, consider transforms m-accretive generalizat...

In this paper, we introduce a new class of functions which are analytic and univalent with negative coefficients defined by using a certain fractional calculus and fractional calculus integral operators. Characterization property,the results on modified Hadamard product and integrals transforms are discussed. Further, distortion theorem and radii of starlikeness and convexity are also determine...